Hydrogen storage in metal hydrides presents distinct challenges which encourage the study of effective heat management strategies. Hydrogen absorption in metal hydrides is an exothermic reaction, consequently the generated heat must be removed effectively to achieve the desired performance. This work presents a mathematical model describing the adsorption of hydrogen in La Ni4.7Co0.3 metal hydride as a storage material. Heat and mass transfer effects are modeled in detail. The effect of heat transfer coefficient is also estimated. Besides, a heat transfer fluid for cooling is incorporated to the model. The problem is mathematically formulated presenting a numerical simulation of a design of a cylindrical tank for hydrogen storage. The alloy is studied by using pressure-composition-temperature curves which are carried out at different temperatures. Thermodynamic parameters and hydrogen storage capacity are determined. For isotherm's kinetics, the Jonhson-Mehl-Avrami-Kolomogorov model is used, from which the kinetic constant of the hydriding process is determined.